Coherence Theory for Finite Holomorphic Maps

  • Hans Grauert
  • Reinhold Remmert
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 236)


In this chapter it is shown that for every finite holomorphic map f: XY the image functor f * is exact in the category of coherent O X -sheaves. It is further proved that if S is a coherent O X -sheaf, then f *(S) is coherent. These two theorems are important ingredients in the proof of Theorem B (see Chapter IV, 1.2).


Abelian Group Structure Sheaf Coherent Sheaf Coherence Theory Image Sheaf 
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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Hans Grauert
    • 1
  • Reinhold Remmert
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenFederal Republic of Germany
  2. 2.Mathematisches InstitutWestfälischen Wilhelms-UniversitätMünsterFederal Republic of Germany

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